Published 2013
| Version v1
Publication
An extension of Mercer theorem to matrix-valued measurable kernels
Description
We extend the classical Mercer theorem to reproducing kernel Hilbert spaces whose elements are functions from a measurable space X into Cn. Given a finite measure μ on X, we represent the reproducing kernel K as a convergent series in terms of the eigenfunctions of a suitable compact operator depending on K and μ. Our result holds under the mild assumption that K is measurable and the associated Hilbert space is separable. Furthermore, we show that X has a natural second countable topology with respect to which the eigenfunctions are continuous and such that the series representing K uniformly converges to K on compact subsets of X×X, provided that the support of μ is X.
Additional details
- URL
- http://hdl.handle.net/11567/376523
- URN
- urn:oai:iris.unige.it:11567/376523
- Origin repository
- UNIGE